Characteristic values of T-filters
type: Item
instance of: scholarly article
title: Characteristic values of T-filters
zbMATH Open document ID: 1087.54003
author: Javier Gutiérrez García
author: María Angeles de Prada Vicente
published in: Fuzzy Sets and Systems
publication date: 2006-01-24T00:00:00Z
review text: Let \((L, \leq, *)\) be a complete MV-algebra, \(X\) be a set. A \(\top\)-filter on \(X\) is a subset of \(L^X\) with certain conditions and an \(L\)-filter on \(X\) is a function \(L^X\longrightarrow L\) with certain conditions. Both \(\top\)-filter and \(L\)-filter can be employed to establish convergence theories in \(L\)-topological spaces. In this paper, the authors extend the notion of characteristic value for prefilters introduced in [\textit{R. Lowen}, General Topology Appl. 10, 147-160 (1979; Zbl 0409.54008)] to every subset of \(L^X\), and then obtain a simple postulation of \(\top\)-filters. The interesting relationship among \(\top\)-filters, \(L\)-filters, and \(L\)-filters of ordinary sets is also discussed.
reviewed by: Dexue Zhang
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 06D35
Mathematics Subject Classification ID: 54A20
zbMATH DE Number: 5001335
zbMATH Keywords: \(\top\)-filter
zbMATH Keywords: prefilter
zbMATH Keywords: characteristic value
zbMATH Keywords: MV-algebra
zbMATH Keywords: \(L\)-filter
MaRDI profile type: Publication
full work available at URL: j.fss.2005.04.012
OpenAlex ID: W2009822323
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DOI: 10.1016/J.FSS.2005.04.012
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description: scientific article; zbMATH DE number 5001335